Heat the oil in a saucepan.
Add the leeks and some salt and saute over medium-low heat until the leeks start to wilt.
Add the cilantro, garlic and pepper. Stir well and allow the leeks to cook until quite tender.
Add 3 cups of water, or enough to almost cover the leeks. Add the potatoes. Bring to a boil and simmer, around 2-3 minutes. Turn off the heat.
If you have an immersion blender, get it out and blitz the soup to a smooth puree right in the pot. If not, add it to a blender (not a food processor), in batches if needed, and blend.
Return the soup to the saucepan and warm through. Add the soymilk if using, and check for seasoning. Add more salt if needed.